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f(x)=3x^(2)-10+18 x

f(x)=3x2−10+18x f(x)=3 x^{2}-10+18 x

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Full solution

Q. f(x)=3x2−10+18x f(x)=3 x^{2}-10+18 x
  1. Identify Quadratic Function: Identify the quadratic function in standard form.\newlinef(x)=3x2+18x−10f(x) = 3x^2 + 18x - 10
  2. Find Vertex X-coordinate: Find the x-coordinate of the vertex using the formula −b2a-\frac{b}{2a}.\newlineFor f(x)=3x2+18x−10f(x) = 3x^2 + 18x - 10, a=3a = 3 and b=18b = 18.\newlinex=−182⋅3x = -\frac{18}{2\cdot 3}\newlinex=−186x = -\frac{18}{6}\newlinex=−3x = -3
  3. Calculate Y-coordinate: Calculate the y-coordinate by plugging the x-coordinate back into the function.\newlinef(−3)=3(−3)2+18(−3)−10f(-3) = 3(-3)^2 + 18(-3) - 10\newlinef(−3)=3(9)−54−10f(-3) = 3(9) - 54 - 10\newlinef(−3)=27−54−10f(-3) = 27 - 54 - 10\newlinef(−3)=−27−10f(-3) = -27 - 10\newlinef(−3)=−37f(-3) = -37
  4. Combine Coordinates for Vertex: Combine the xx and yy coordinates to get the vertex of the parabola.\newlineVertex = (−3,−37)(-3, -37)

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